Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #452 |
| Sylow | C5 ⋊ #5047 |
| Sylow | C3 ⋊ #65528 |
304 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^4,d^b=df,g^b=g^2105 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5047, D3×#65528, #14423524, … |
| maximal normal subgroup of | D5×#5047, D3×#65528, #14423524, … |
| maximal quotient of | #14288070, #14288211, #14288634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2733);